Real-time feedback control method for arrayed wave energy conversion devices

Abstract

This invention proposes a real-time feedback control method for arrayed wave energy conversion devices. The method includes numerical modeling and hydrodynamic analysis of the arrayed wave energy conversion device, establishing its temporal motion equation and spatial state equation, replacing the convolution term of the temporal motion equation with the state-space equation to obtain its motion state, combining wave spectrum characteristics with the hydrodynamic response characteristics of the floats, comprehensively considering the hydrodynamic interference between floats in the array system, constructing a causal mapping relationship between float velocity and wave excitation force, thereby calculating the desired float response velocity, and applying control force to the PTO through feedback control to maintain the device in a near-optimal resonance state under random wave action, making the velocity of each float close to the optimal functional extraction condition for each wave frequency, thus achieving efficient real-time extraction of wave energy.

Description

Technical Field

[0001] This invention belongs to the field of wave energy power generation technology, specifically, it relates to a real-time feedback control method for arrayed wave energy conversion devices. Background Technology

[0002] Against the backdrop of an accelerating global energy transition, the development of marine renewable energy has become a strategic area for energy technology innovation. Wave energy, with its wide distribution, high energy density, and unique advantages of being able to power marine infrastructure in tandem, is widely recognized as one of the most promising blue energy sources. Its core component, the Wave Energy Converter (WEC), uses energy-capturing elements such as floats and pendulum mechanisms to convert the kinetic energy of ocean waves into mechanical energy, ultimately outputting electricity through a power system. It has already demonstrated application potential in areas such as powering remote islands and supplying energy to marine ranches.

[0003] Although various energy capture configurations have emerged in the field of wave energy conversion devices, their average energy conversion efficiency is still relatively low. After wave energy capture, how to achieve high-efficiency wave energy absorption remains a key technology for wave power generation. Summary of the Invention

[0004] The purpose of this invention is to propose a real-time feedback control method for arrayed wave energy conversion devices. This method constructs a causal mapping relationship between buoy velocity and wave excitation force, solves the causal transfer function between wave excitation force and buoy velocity, calculates the desired buoy response velocity using the causal transfer function between wave excitation force and buoy velocity and the current wave excitation force, and applies a control force to the PTO through feedback control to maintain the device in a near-optimal resonance state under the action of random waves, thereby achieving efficient real-time extraction of wave energy.

[0005] The present invention is implemented using the following technical solutions:

[0006] A real-time feedback control method for arrayed wave energy conversion devices is proposed, including:

[0007] S1, Numerical modeling and hydrodynamic analysis of arrayed wave energy conversion device;

[0008] S2: Establishing the time-domain motion equations of the wave energy conversion device based on impulse response theory;

[0009] S3: Establish the state-space equation of the arrayed wave energy conversion device, replace the convolution term of the time-domain motion equation with the state-space equation, and calculate the motion state of the arrayed wave energy conversion device.

[0010] S4, construct the wave excitation force and buoy velocity transfer function, calculate the target buoy velocity response based on the current wave excitation force, and extract the actual velocity of the buoy from the calculated motion state. Based on the deviation between the actual velocity and the target buoy velocity, control the arrayed wave energy conversion device to extract wave energy, including:

[0011] Extracting power from arrayed wave energy conversion devices:

[0012] , ;in, The wave excitation force-buoy velocity transfer function, The desired float velocity response;

[0013] Wave excitation force; Let be the wave force transfer function. For the spectrum; Z represents the system's inherent impedance;

[0014] Define the second term in P as the loss function, and we get

[0015] This transforms the power conversion problem into a problem of finding the minimum value of the loss function;

[0016] make The loss function affects the transfer function. The optimal value is obtained by setting the first partial derivative to zero. ;in,

[0017] , ;

[0018] based on The optimal value and the current wave excitation force are used to obtain the target velocity response. The actual velocity of the float is extracted from the calculated motion state. The deviation between the actual velocity and the target velocity is transmitted to the PID control module so that the PID control module controls the arrayed wave energy conversion device to extract wave energy.

[0019] In some embodiments of the present invention, the time-domain motion equations established in S2 are as follows:

[0020] ,

[0021] ;

[0022] Among them, M1 and M2 are the masses of the two wave energy conversion devices, respectively; 11 and 22These are the additional masses of the two wave energy conversion devices, 12 and 21 The effects of the motion of one wave energy conversion device on the additional inertial force generated by the heave direction on another wave energy conversion device are respectively: These are the displacement, velocity, and acceleration of the two wave energy conversion devices, respectively. It is the delay function representing the radiative interaction. It is radiation damping. These represent the self-radiation delay functions of the two wave energy conversion devices, respectively, and indicate the historical influence of the radiation waves generated by the device's own motion on its own velocity. Let F represent the delay function of the radiation effect of the motion of one wave converter on the other wave converter; K is the still water restoring stiffness. e,1 and F e,2 These are the wave excitation forces of the first wave energy conversion device and the second wave energy conversion device, respectively. The calculation formula is as follows: Re denotes taking the real part of a complex function. Let be the transfer function of the wave-induced vibration force. For the spectrum, For wave frequency, For wave random phase; The force provided by the PTO system to the wave energy conversion device.

[0023] In some embodiments of the present invention, the state-space equation established by S3 is as follows:

[0024] ,

[0025] ,

[0026] ;

[0027] in, Represents an n×1 dimensional state variable. , , The terms used to approximate the convolution term represent the n×n, n×1, and 1×n state space matrices, respectively, which are calculated using the system identification method.

[0028] In some embodiments of the present invention, in S3, a new state variable is defined.

[0029] Substituting the established state-space equations into the time-domain equations of motion and transforming them into linear differential equations:

[0030] ;

[0031] The motion state of the arrayed wave energy conversion device is obtained by solving the linear differential equation using the fourth Runge-Kutta method.

[0032] in,

[0033] ,

[0034] ,

[0035] ,

[0036] ;

[0037] ,

[0038] .

[0039] In some embodiments of the present invention, S4 extracts the power of the arrayed wave energy conversion device, including:

[0040] Power extraction from arrayed wave energy conversion devices:

[0041] ;in, This indicates the load capacity provided by the PTO device. This indicates the velocity response of the float;

[0042] Based on the inherent impedance of the arrayed wave energy conversion device Mathematical transformation of the power extraction formula:

[0043] ;

[0044] The mathematical equivalent transformation simplifies it to:

[0045] .

[0046] In some embodiments of the present invention, in S4, according to the principle of minima, the first-order partial derivative of a function being zero is a necessary condition for reaching a minimum. Therefore, the loss function LOSS is applied to the transfer function... Find the partial derivative:

[0047] ,

[0048] Based on the basic rules of differentiation, the original expression is decomposed.

[0049] ,

[0050] Integration

[0051] ,

[0052] According to the principle of minima, let the first-order partial derivative of the loss function with respect to the transfer function be zero.

[0053] ,

[0054] get .

[0055] Compared with existing technologies, the advantages and positive effects of this invention are as follows: The real-time feedback control method for arrayed wave energy conversion devices proposed in this invention combines wave spectrum characteristics with the hydrodynamic response characteristics of the floats, comprehensively considers the hydrodynamic interference between floats in the array system, constructs a causal mapping relationship between float velocity and wave excitation force, calculates the desired float response velocity, and applies control force to the PTO through feedback control, enabling the device to maintain a near-optimal resonance state under random wave action, making the velocity of each float approach the optimal functional extraction condition for each wave frequency, thus achieving efficient real-time extraction of wave energy. The method of this invention exhibits significant advantages in power absorption, not only effectively improving the overall energy absorption capacity of the arrayed wave energy conversion device but also providing counting support for the operation of large-scale wave energy arrays. This method has a simple structure, clear physics, and is easy to implement in engineering, making it particularly suitable for the design of control systems for wave energy arrays. Attached Figure Description

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 The steps of the real-time feedback control method for the arrayed wave energy conversion device proposed in this invention are as follows:

[0058] Figure 2 This is a schematic diagram of the structure of an arrayed wave energy conversion device;

[0059] Figure 3 This invention relates to the control principle of the arrayed wave energy conversion device.

[0060] Figure 4 This is a comparison chart of the wave energy capture efficiency of the method of the present invention with that of the existing uncontrolled transfer function method that considers mutual hydrodynamic interference.

[0061] Figure 5 The example diagram illustrates the specific implementation of the working condition, where the random wave environment is based on a random wave spectrum generated by jonswap. Detailed Implementation

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0063] When a wave energy conversion device (hereinafter referred to as the wave energy device or device) is in a resonant state, the wave force acting on the device and the device's velocity are completely in phase. At this time, the waves always do positive work on the device, and the wave energy captured by the device is maximized. Therefore, resonance is an effective method to improve the energy capture efficiency of wave energy devices.

[0064] To achieve efficient wave energy absorption, the applicant proposed a latching control strategy based on the optimal resonant phase principle in a previous application. This strategy involves periodically locking or releasing the wave energy device through an external mechanism to adjust its motion state, reduce the system's oscillation frequency, and thus ensure that the float's velocity phase is consistent with the wave excitation force. This strategy is suitable for wave energy devices with a natural frequency higher than the wave frequency. In contrast, a declutching control strategy was developed for devices with a natural frequency lower than the wave frequency. Although both strategies can ensure the system meets the optimal phase condition, they are not optimal control strategies because their control force is discontinuous and they do not consider amplitude matching.

[0065] In contrast, Complex Conjugate Control (CCC), also known as Reactive Control, continuously applies control force to the device through a power take-off (PTO) system, maintaining the buoy and wave excitation force in an optimal resonance state. Theoretically, this can achieve maximum power capture and represents the current optimal control strategy. However, this strategy uses the complex conjugate of the system's inherent impedance as the basis for the optimal load impedance. While inherent impedance is defined as a complex function in the frequency domain, the control process must be implemented in the time domain. Mapping the frequency domain impedance to the time domain requires introducing an integral control term in the form of a convolution kernel. This convolution kernel inevitably depends on future buoy velocity information, resulting in CCC exhibiting non-causal control in the time domain. Specifically, the integral control component in CCC is completely non-causal; its implementation requires predicting the future state of the wave energy device, limiting its real-time performance and engineering feasibility.

[0066] Therefore, how to maintain high energy absorption efficiency while avoiding dependence on future states and constructing a causal optimal or suboptimal control method has become a key issue in current wave energy control research.

[0067] This invention aims to overcome the aforementioned technical bottlenecks by proposing a wave force-buoy velocity control strategy based on a causal transfer function. This method combines local wave spectrum characteristics with the hydrodynamic response characteristics of the buoy, comprehensively considering the hydrodynamic interference effects between buoys in the array system, and constructs a causal mapping relationship between buoy velocity and wave excitation force. The desired buoy response velocity is then calculated, and a control force is applied to the PTO (Potentially Oscillating Toll Collection) using feedback control methods (such as PID control), enabling the device to maintain a near-optimal resonance state under random wave action, achieving efficient real-time extraction of wave energy. This method has a simple structure, clear physics, and is easy to implement in engineering, making it particularly suitable for the design of control systems for wave energy arrays.

[0068] The following example uses an arrayed wave energy conversion device comprising two wave energy conversion devices (more than two cases can be implemented and expanded based on the concept of this embodiment), combined with... Figure 3 The control principle described herein explains the real-time feedback control method proposed in this invention.

[0069] like Figure 1 As shown, the method includes the following steps:

[0070] S1: Numerical modeling and hydrodynamic analysis of arrayed wave energy conversion devices.

[0071] The arrayed wave energy conversion device consists of two identical and coordinated oscillating float-type wave energy conversion devices. This type of device captures the kinetic energy of waves by the reciprocating motion of a float, and then uses a power output system (PTO) to drive a generator to produce electricity. The float, connecting rod, and PTO system are its main components. The float is connected to the PTO system via the connecting rod. PTO systems mainly include hydraulic, mechanical transmission, hydraulic-driven, pneumatic, linear motor, and hybrid hydraulic types. This invention selects a hydraulic PTO system, which mainly includes a hydraulic cylinder, a hydraulic motor, and a generator. The piston rod of the hydraulic cylinder is connected to the connecting rod, the hydraulic cylinder drives the hydraulic motor, and the hydraulic motor drives the generator to produce electricity.

[0072] Furthermore, the working principle of the oscillating float-type wave energy conversion device is as follows: Under the periodic motion of the waves, the float drives the piston in the hydraulic cylinder to reciprocate vertically through the connecting rod. This reciprocating motion increases the oil pressure by compressing and releasing the hydraulic oil in the hydraulic cylinder, thereby converting the mechanical energy of the waves into hydraulic energy. Subsequently, the high-pressure hydraulic oil flows through pipelines, driving the hydraulic motor, which further converts the hydraulic energy into rotational mechanical energy (i.e., the torque and speed of the output shaft). The rotational motion of the output shaft then drives a three-phase permanent magnet synchronous generator, whose working principle is based on the law of electromagnetic induction. When the mechanical energy causes the rotor inside the generator to rotate, the permanent magnets installed on the rotor rotate accordingly, cutting the magnetic field in the stator coils. Since the stator coils consist of three-phase coils, the rotating magnetic field of the rotor generates three-phase alternating current with a phase difference of 120° in each group of coils. The characteristic of this power generation method is that the rotor speed and the frequency of the output current remain synchronized, ensuring a stable current output. Meanwhile, because permanent magnets do not require an external excitation source, three-phase permanent magnet synchronous generators are highly efficient, simple in structure, and have low maintenance costs, making them very suitable for the long-term operation of wave energy conversion devices. This entire process achieves efficient conversion from wave mechanical energy to electrical energy.

[0073] In this invention, combined Figure 2 As shown, the arrayed wave energy conversion device consists of two identical oscillating float-type wave energy conversion devices (wave energy conversion device 1 and wave energy conversion device 2). Wave energy conversion devices 1 and 2 are mainly composed of float 11, connecting rod 12, and PTO 13. Float 11 is a cylindrical float with a radius of 2.5m and a draft of 5m. PTO 13 adopts a hydraulic PTO system, mainly composed of piston rod, hydraulic cylinder, hydraulic motor, and generator. The piston rod of the hydraulic cylinder is connected to the connecting rod 12. The hydraulic cylinder drives the hydraulic motor to operate, and the hydraulic motor drives the generator to generate electricity. Float 11 moves in the wave... Under the action of the wave energy converter, it reciprocates in the heave direction and is connected to the PTO13 via the connecting rod 12. The connecting rod 12 drives the piston of the hydraulic cylinder to move up and down in the heave direction, increasing the pressure of the hydraulic oil in the hydraulic cylinder cavity. This process converts mechanical energy into hydraulic energy. The hydraulic oil then drives the hydraulic motor, converting the liquid pressure energy in the pipeline into the mechanical energy (torque and speed) of the output shaft, which then drives the generator at the rear end to generate electrical energy. The generator uses existing equipment: a three-phase permanent magnet synchronous motor. The wave energy conversion device 2 mainly consists of a float 21, a connecting rod 22 and a hydraulic PTO23, and its working principle is the same as that of the wave energy conversion device 1.

[0074] This invention utilizes the GeniE module in DNV-GL SESAM software to establish a numerical model of a wave energy conversion device that only includes the portion below the waterline, because only the hydrodynamic effects on the portion of the float below the waterline are considered.

[0075] The specific modeling process is as follows:

[0076] (1) Construct the geometric model of the float by points, lines and surfaces, and build a wave energy array numerical model with a radius of 2.5m and a draft of 5m;

[0077] (2) Define the wetted surface of the dual-unit wave energy array;

[0078] (3) Apply a load to the wetted surface of the dual-unit wave energy array;

[0079] (4) Divide the grid, and set the grid size to 0.1m;

[0080] (5) Run the analysis and generate the .fem file.

[0081] After obtaining the .fem file, import it into the hydroD module for frequency domain hydrodynamic analysis. The specific analysis process is as follows:

[0082] (1) Define environmental parameters, such as the direction and frequency range of waves, as well as the draft, center of buoyancy, and center of gravity of the floating body;

[0083] (2) Create a hydrodynamic model;

[0084] (3) Import the .fem panel model file;

[0085] (4) Create a quality model;

[0086] (5) Operational analysis;

[0087] (6) Result viewing and post-processing to obtain the hydrodynamic parameters of the wave energy conversion device.

[0088] S2: Establish the time-domain motion equation of the wave energy conversion device based on impulse response theory.

[0089] A right-handed coordinate system fixed on Earth is used, with its center at the mean sea level. The Z-axis is positive upwards, and the X-axis represents the direction of wave propagation. The time-domain motion equations of the arrayed wave energy conversion device are as follows:

[0090] ;

[0091] Expanding this into the equations of motion for a multi-degree-of-freedom float:

[0092] ;

[0093] ,

[0094] ;

[0095] in, and These are the masses of the two wave energy conversion devices; 11 and 22 These are the additional masses of the two wave energy conversion devices, 12 and 21 The effects of the motion of one wave energy conversion device on the additional inertial force generated by the heave direction on another wave energy conversion device are respectively: These are the displacement, velocity, and acceleration of the two wave energy conversion devices, respectively. It is the delay function representing the radiative interaction. It is radiation damping. These represent the self-radiation delay functions of the two wave energy conversion devices, respectively, and indicate the historical influence of the radiation waves generated by the device's own motion on its own velocity. Let represent the delay function of the radiation effect of the motion of one wave converter on the other wave converter; K is the still water restoring stiffness. The force provided by the PTO system to the wave energy conversion device; and These are the wave excitation forces of the first wave energy conversion device and the second wave energy conversion device, respectively. The calculation formulas are shown below:

[0096] ;

[0097] Re denotes taking the real part of a complex function. Let be the transfer function of the wave-induced vibration force. For the spectrum, For wave frequency, For the random phase of the wave.

[0098] The aforementioned hydrodynamic parameters, such as the added mass at infinite frequency Wave force transfer function All results were calculated using the hydrodynamic analysis software SESAM-WADAM.

[0099] S3: Establish the state-space equation of the arrayed wave energy conversion device, replace the convolution term of the time-domain motion equation with the state-space equation, and calculate the motion state of the arrayed wave energy conversion device.

[0100] The state-space equation is shown in formula (5):

[0101] , , ;

[0102] Using the approximation formula of linear differential equations In The linear differential equation is as shown in the formula. As shown:

[0103] ;

[0104] Combining formulas (5) and (6), we can obtain formula (7).

[0105] , , ;

[0106] in, Represents an n×1 dimensional state variable. , , The terms used to approximate the convolution term are denoted by n×n, n×1, and 1×n state space matrices, respectively, and their expansions are... It was calculated using a system identification method.

[0107] Specifically, let's first look at linear differential equations. Performing a Laplace transform yields:

[0108] ;

[0109] For the delay function representing the radiative interaction Performing a Fourier transform yields:

[0110] ;

[0111] Again Performing a Fourier transform yields:

[0112] ;

[0113] Combining formulas and ,get:

[0114] ;

[0115] calculate get:

[0116] ,

[0117] ;

[0118] in, These are radiation damping and added mass, respectively, calculated using the hydrodynamic software Hydrod. Then, p and q are calculated according to formula (12), and thus... , , .

[0119] The above, molecular coefficient group With the denominator coefficient group The target frequency response function is obtained through least squares fitting. The extracted values ​​are used to construct a class of rational transfer functions, aiming to approximate the dynamic characteristics of the original radiative memory kernel function in the complex frequency domain (i.e., as shown in formula (12), the original radiative memory kernel function). The real part represents radiation damping, and the imaginary part is divided by... (Represents added mass).

[0120] State space equations of wave energy array Substitute the time-domain motion equations of the float and define new state variables:

[0121] ;

[0122] The time-domain equation of motion of the wave energy array can then be rewritten as a linear differential equation:

[0123] ;

[0124] Define the initial condition X(0) = 0, and use the fourth Runge-Kutta method to solve the formula. The motion state X of the arrayed wave energy conversion device can be obtained through calculation.

[0125] The specific solution steps are as follows:

[0126] ;

[0127] in, This indicates the viscous damping of the system (critical damping is 1%). The density of water, Let M be the acceleration due to gravity, M be the mass of the float, and μ be the additional mass at an infinite frequency. To restore stiffness to still water.

[0128] Perform matrix operations on the above expression to transform it into... :

[0129] ;

[0130] ,

[0131] ,

[0132] , ,

[0133] ,

[0134] .

[0135] The state-space equations of the arrayed wave energy conversion device are solved using the fourth Runge-Kutta method to obtain the motion state of the arrayed wave energy conversion device.

[0136] S4: Construct the wave excitation force and float velocity transfer function, calculate the target float velocity response based on the current wave excitation force, extract the actual velocity of the float from the calculated motion state, and control the arrayed wave energy conversion device to extract wave energy based on the deviation between the actual velocity and the target float velocity.

[0137] The wave force-buoy velocity coupling control strategy described in this invention belongs to complex conjugate control. Its core idea is to ensure that the velocity of the energy harvesting device (i.e., the wave energy conversion device) is in phase with the wave excitation force. By applying continuous control force to the PTO through feedback control, the system force (referring to the reaction force naturally generated by the wave energy conversion device itself in the wave, including radiation damping force, added mass force and restoring force, which together hinder the free movement of the buoy) is eliminated to achieve resonance. Moreover, the optimal load impedance is equal to the complex conjugate of the system's inherent impedance. At this time, the device's harvesting power can reach the theoretical maximum value. Therefore, complex conjugate control is the optimal control method.

[0138] Since the optimal load impedance is equal to the complex conjugate of the system's intrinsic impedance, and the system's intrinsic impedance is essentially a complex function defined in the frequency domain, it must be mapped from the frequency domain to the time domain when used in a control strategy. This mapping process corresponds to the introduction of a time-domain convolution kernel, which typically contains dependencies on future system states (such as float velocity).

[0139] In other words, complex conjugate control establishes the optimal energy absorption conditions in the frequency domain, but its control command in the time domain, namely the control force applied by PTO, needs to be based on the convolutional response derived from the frequency domain impedance. Since this convolutional kernel involves the weighted integral of future velocities, the controller must know the future motion state of the system at the current moment, and thus needs to predict future wave excitations.

[0140] Therefore, complex conjugate control strategies are inherently non-causal, and their non-causality mainly stems from their dependence on future states. This characteristic constitutes an obstacle to the widespread application of complex conjugate control in practical engineering. To overcome this problem, this invention proposes a wave force-buoy velocity dynamic coupling control strategy based on a causal transfer function. The method of this invention does not require prediction of future wave excitation, but instead constructs a causal transfer function through rigorous theoretical derivation to realize a direct mapping relationship between the current wave excitation force and the desired buoy velocity response. This effectively avoids the non-causal problem in traditional optimal control strategies and provides a practical solution for the real-time control and engineering implementation of wave energy arrays.

[0141] The power extraction of arrayed wave energy conversion devices is calculated according to the following formula:

[0142] ;

[0143] in, This indicates the load capacity provided by the PTO device. This indicates the velocity response of the float, and * indicates complex conjugate.

[0144] Based on the inherent impedance of the arrayed wave energy conversion device:

[0145] ;

[0146] For the formula Perform mathematical transformations:

[0147] ;

[0148] Where Z represents the system's inherent impedance. This indicates the excitation force of the waves.

[0149] Combining formulas and A mathematical equivalent transformation is performed on the power extraction of the wave energy conversion device:

[0150] ,

[0151] ,

[0152] ;

[0153] make The power extraction from wave energy conversion devices can be simplified as follows:

[0154] ;

[0155] ;

[0156] The wave excitation force-buoy velocity transfer function. The desired float velocity response.

[0157] If the equation (22) is met, it means that the speed of the wave energy conversion device is in phase with the wave excitation force, and resonance is achieved. The optimal load impedance is equal to the complex conjugate of the inherent impedance of the system. At this time, the power captured by the device can reach the theoretical maximum value.

[0158] For given wave conditions, the formula The first term is a constant, and the second term is positioned as the loss function. The energy capture power of the wave energy conversion device is maximized when the loss reaches its minimum value. Combining formulas (21) and (22), the loss function is expressed mathematically as follows:

[0159] ;

[0160] The wave excitation force is expressed as:

[0161] ;

[0162] Let be the wave force transfer function. For the spectrum, This is the wave energy-buoy velocity transfer function.

[0163] Through formula , right Transform the loss function:

[0164] ;

[0165] ;

[0166] The power conversion problem of the wave energy conversion device is then transformed into a problem of finding the minimum value of the loss function.

[0167] make ,but

[0168] .

[0169] According to the principle of minima, the first-order partial derivative of a function being zero is a necessary condition for finding a minimum. Therefore, from the loss function... right Find the partial derivative:

[0170] ;

[0171] Based on the basic rules of differentiation, the original expression can be broken down as follows:

[0172] ;

[0173] Based on the rules for matrix differentiation of scalar functions as described in The Matrix Cookbook, the original expression is integrated as follows:

[0174] ;

[0175] According to the principle of minima, let the first-order partial derivative of the loss function with respect to the transfer function be zero.

[0176] ;

[0177] ;

[0178] , It is an asymmetric matrix; , It is a symmetric matrix.

[0179] That is, when the wave excitation force - buoy velocity transfer function For formula When taking values, the loss function right The partial derivatives being all zero is a necessary condition for the point to reach a local minimum.

[0180] According to the principle of minima, the first-order partial derivatives of all components of a multivariate function are 0, and the Hessian matrix of the function is positive definite; this is the point of minimum.

[0181] ;

[0182] ;

[0183] Performing row and column transformations on a Hessian matrix does not change the matrix's positive definiteness:

[0184] ;

[0185] Since the positive definiteness of a block diagonal matrix is ​​determined by the positive definiteness of each diagonal sub-block, the positive definiteness of a Hessian matrix depends on the positive definiteness of matrix A.

[0186] ;

[0187] in:

[0188] , , , , ;

[0189] Therefore, formula (34) can be expanded as follows:

[0190] ;

[0191] According to the necessary and sufficient condition for the positive definiteness of a matrix, if all principal minors of order 1 are greater than 0, then the matrix is ​​positive definite. (Formula) middle:

[0192] ;

[0193] ;

[0194] From the formula , As shown, matrix A is always positive definite, and the positive definiteness of the block matrix implies that the Hessian matrix is ​​also always positive definite.

[0195] Therefore The loss function is minimized when the wave energy absorption efficiency is maximized.

[0196] Specifically, when the loss function reaches its minimum value, i.e., when the energy loss is minimal, the wave energy absorption efficiency is maximized. It is worth noting that although the absorption efficiency of the array-type wave energy device is maximized at this point, the absorption efficiency of a single device is not optimal; rather, it improves the overall absorption efficiency. At this point, the expected float response obtained from the wave force-buoy velocity transfer function is not the optimal float oscillation speed, but a suboptimal control that approximates the causal relationship as closely as possible.

[0197] To achieve the maximum power generation of the arrayed wave energy conversion device, the optimal value of the transfer function between wave excitation force and float velocity is obtained by constructing a loss function LOSS and minimizing it in alignment, as shown in formula (31). This transfer function is used to characterize the optimal float velocity response and the transfer relationship between wave excitation force that the device should achieve under a given wave excitation.

[0198] Based on the wave excitation force experienced by each float in the array at the current moment, the target velocity response of each float is calculated according to the transfer function as shown in formula (22). Further, combined with the actual motion state of the device obtained in real time in S3, the actual velocity of the float is extracted, and the deviation between the actual velocity and the target velocity is used as input and transmitted to the PID control module. The PID module uses the velocity deviation as feedback signal and outputs control commands, namely the mechanical force of the PTO device, to form a closed-loop control, thereby realizing the dynamic adjustment and optimal guidance of the motion state of the device, thereby improving the energy capture efficiency and approaching the theoretical optimal functional absorption state.

[0199] In a specific embodiment of the present invention, numerical simulations were performed on an arrayed system consisting of two wave energy converters, under controlled and transfer function-based control strategies, to compare their energy capture performance. The incident wave was described using the JONSWAP spectrum. Taking case one as an example, its effective wave height Hs is 2m, the peak period Tp is 6s, and the required constant value λ=3 for the JONSWAP spectrum is 3. Cases two and three only adjust the effective wave height and peak period, such as... Figure 4 As shown. The total simulation duration is 3600s, and the sampling time interval is 0.01s.

[0200] Figure 5 The graph compares the one-hour wave energy capture efficiency under different operating conditions with and without control using a transfer function-based control strategy. Taking operating condition one as an example, without control, the average energy capture power of the wave energy conversion device is 14 kW per hour. However, when the transfer function-based control strategy is applied, the average energy capture power per hour is 142 kW. Compared to the uncontrolled case, the transfer function-based control algorithm increases the energy capture efficiency by 914.28%. This demonstrates that the transfer function-based control algorithm proposed in this invention can significantly improve wave energy capture efficiency, exhibiting superior performance advantages.

[0201] It should be noted that the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A real-time feedback control method for an arrayed wave energy conversion device, characterized in that, include: S1, Numerical modeling and hydrodynamic analysis of arrayed wave energy conversion device; S2: Establishing the time-domain motion equations of the wave energy conversion device based on impulse response theory; S3: Establish the state-space equation of the arrayed wave energy conversion device, replace the convolution term of the time-domain motion equation with the state-space equation, and calculate the motion state of the arrayed wave energy conversion device. S4, construct the wave excitation force and buoy velocity transfer function, calculate the target buoy velocity response based on the current wave excitation force, and extract the actual velocity of the buoy from the calculated motion state. Based on the deviation between the actual velocity and the target buoy velocity, control the arrayed wave energy conversion device to extract wave energy, including: Extracting power from arrayed wave energy conversion devices: , ;in, The wave excitation force-buoy velocity transfer function. The desired float velocity response; Wave excitation force; Let be the wave force transfer function. For the spectrum; ; Indicates the inherent impedance of the system; Define the second term in P as the loss function, and we get This transforms the power conversion problem into a problem of finding the minimum value of the loss function; make The loss function affects the transfer function. The optimal value is obtained by setting the first partial derivative to zero. ;in, ， ； based on The optimal value and the current wave excitation force are used to obtain the target velocity response. The actual velocity of the float is extracted from the calculated motion state. The deviation between the actual velocity and the target velocity is transmitted to the PID control module so that the PID control module controls the arrayed wave energy conversion device to extract wave energy.

2. The real-time feedback control method for an arrayed wave energy conversion device according to claim 1, characterized in that, The time-domain motion equations established in S2 are as follows: ， ； Among them, M1 and M2 are the masses of the two wave energy conversion devices, respectively; 11 and 22 These are the additional masses of the two wave energy conversion devices, 12 and 21 The effects of the motion of one wave energy conversion device on the additional inertial force generated by the heave direction on another wave energy conversion device are respectively: These are the displacement, velocity, and acceleration of the two wave energy conversion devices, respectively. It is the delay function representing the radiative interaction. It is radiation damping. These represent the self-radiation delay functions of the two wave energy conversion devices, respectively, and indicate the historical influence of the radiation waves generated by the device's own motion on its own velocity. Let F and F represent the delay functions of the radiation effect of the motion of one wave converter on the other wave converter, respectively; K is the still water restoring stiffness; F e,1 and F e,2 These are the wave excitation forces of the first wave energy conversion device and the second wave energy conversion device, respectively. The calculation formula is as follows: Re denotes taking the real part of a complex function. Let be the transfer function of the wave-induced vibration force. For the spectrum, For wave frequency, For wave random phase; The force provided by the PTO system to the wave energy conversion device.

3. The real-time feedback control method for an arrayed wave energy conversion device according to claim 2, characterized in that, The state-space equations established by S3 are as follows: ， ， ； in, Represents an n×1 dimensional state variable. , , The terms used to approximate the convolution term represent the n×n, n×1, and 1×n state space matrices, respectively, and are calculated using the system identification method.

4. The real-time feedback control method for an arrayed wave energy conversion device according to claim 3, characterized in that, In S3, define new state variables. Substituting the established state-space equations into the time-domain equations of motion and transforming them into linear differential equations: ； The motion state of the arrayed wave energy conversion device is obtained by solving the linear differential equation using the fourth Runge-Kutta method. in, ， ， ， ； ， 。 5. The real-time feedback control method for an arrayed wave energy conversion device according to claim 1, characterized in that, S4 extracts power from the arrayed wave energy conversion device, including: Power extraction from arrayed wave energy conversion devices: ;in, This indicates the force provided by the PTO system to the wave energy conversion device. This indicates the velocity response of the float; Based on the inherent impedance of the arrayed wave energy conversion device Mathematical transformation of the power extraction formula: ； The mathematical equivalent transformation simplifies it to: 。 6. The real-time feedback control method for an arrayed wave energy conversion device according to claim 5, characterized in that, In S4, according to the minimum principle, a zero first-order partial derivative of a function is a necessary condition for reaching a minimum. Therefore, the loss function LOSS affects the transfer function. Find the partial derivative: ， Based on the basic rules of differentiation, the original expression is decomposed. ， Integration ， According to the principle of minima, let the first-order partial derivative of the loss function with respect to the transfer function be zero. ， get .

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